In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arb...In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.展开更多
高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型...高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型求积单元模型,发展了一种高耸结构P-Δ效应高阶精确分析方法.该方法能够应用于具有突变质量的结构体系,可处理任意轴向荷载引起的动力P-Δ效应问题,无需迭代计算即可获得高精度的P-Δ效应解答,同时能准确地揭示竖向荷载以及时变轴力对高耸结构特性的影响规律.通过对3个不同类型案例的比较分析,验证了本文方法的可行性和准确性.数值分析结果表明,本文方法可以实现高精度的P-Δ效应分析,对于质量均匀分布和含有集中质量的结构体系仅需使用一个求积单元即可获得非常精确的动态响应结果.展开更多
A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this wor...A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.展开更多
在本文中,我们提出了一种修正的高阶有限差分Hermite WENO (HWENO)方法,用于求解均匀网格中的一维和二维对流扩散方程。与求解双曲守恒律的有限差分HWENO方法不同,我们扩展了该方法以求解对流扩散方程。其关键不是使用通量分裂技术,而...在本文中,我们提出了一种修正的高阶有限差分Hermite WENO (HWENO)方法,用于求解均匀网格中的一维和二维对流扩散方程。与求解双曲守恒律的有限差分HWENO方法不同,我们扩展了该方法以求解对流扩散方程。其关键不是使用通量分裂技术,而是使用添加高阶修正项的想法来提高数值通量的精度。此外,在重构过程中,我们不在单元界面上使用函数及其导数值,而是使用解及其导数的点值直接插值。使用Hermite插值计算高阶导数和扩散项,以保持方法的紧凑性。这种方法的一个优点是数值通量的重构过程可以采用任意单调通量。另一个优点是,修改后的方法仍然具有HWENO方案的紧性,并且在相同的网格上也具有更小的数值误差和更好的分辨率。通过一维和二维问题的数值算例验证了所提方法的有效性和稳定性。In this paper, we propose a modified high-order finite difference Hermite WENO (HWENO) method for solving one and two dimensions convection-diffusion equations in uniform meshes. Unlike the finite difference HWENO method for solving hyperbolic conservation laws, we extend the method to solve convection-diffusion equations. The key is not to use the flux splitting technique, but to use the idea of adding higher-order corrections to improve the precision of the numerical flux. Moreover, in the reconstruction process, we do not use the function and its derivative values on the cell interface, but use the direct interpolation of the point values of the solution and its derivatives. The higher derivatives and diffusion term are computed using Hermite interpolation to maintain the compactness of the method. An advantage of this method is that the reconstruction process of the numerical flux can adopt any monotone flux. Another advantage is that the modified method still has the compactness of the HWENO schemes, and also has smaller numerical errors and better resolution on the same mesh. The validity and stability of the proposed method are verified by numerical examples of one and two dimensions problems.展开更多
基金This work was supported by the National Basic Research Program of China （No.2013CB922200）, the National Natural Science Foundation of China （No.21222308, No.21103187, and No.21133006）, the Chinese Academy of Sciences, and the Key Research Program of the Chinese Academy of Sciences.
文摘In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.
文摘高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型求积单元模型,发展了一种高耸结构P-Δ效应高阶精确分析方法.该方法能够应用于具有突变质量的结构体系,可处理任意轴向荷载引起的动力P-Δ效应问题,无需迭代计算即可获得高精度的P-Δ效应解答,同时能准确地揭示竖向荷载以及时变轴力对高耸结构特性的影响规律.通过对3个不同类型案例的比较分析,验证了本文方法的可行性和准确性.数值分析结果表明,本文方法可以实现高精度的P-Δ效应分析,对于质量均匀分布和含有集中质量的结构体系仅需使用一个求积单元即可获得非常精确的动态响应结果.
文摘A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.
文摘在本文中,我们提出了一种修正的高阶有限差分Hermite WENO (HWENO)方法,用于求解均匀网格中的一维和二维对流扩散方程。与求解双曲守恒律的有限差分HWENO方法不同,我们扩展了该方法以求解对流扩散方程。其关键不是使用通量分裂技术,而是使用添加高阶修正项的想法来提高数值通量的精度。此外,在重构过程中,我们不在单元界面上使用函数及其导数值,而是使用解及其导数的点值直接插值。使用Hermite插值计算高阶导数和扩散项,以保持方法的紧凑性。这种方法的一个优点是数值通量的重构过程可以采用任意单调通量。另一个优点是,修改后的方法仍然具有HWENO方案的紧性,并且在相同的网格上也具有更小的数值误差和更好的分辨率。通过一维和二维问题的数值算例验证了所提方法的有效性和稳定性。In this paper, we propose a modified high-order finite difference Hermite WENO (HWENO) method for solving one and two dimensions convection-diffusion equations in uniform meshes. Unlike the finite difference HWENO method for solving hyperbolic conservation laws, we extend the method to solve convection-diffusion equations. The key is not to use the flux splitting technique, but to use the idea of adding higher-order corrections to improve the precision of the numerical flux. Moreover, in the reconstruction process, we do not use the function and its derivative values on the cell interface, but use the direct interpolation of the point values of the solution and its derivatives. The higher derivatives and diffusion term are computed using Hermite interpolation to maintain the compactness of the method. An advantage of this method is that the reconstruction process of the numerical flux can adopt any monotone flux. Another advantage is that the modified method still has the compactness of the HWENO schemes, and also has smaller numerical errors and better resolution on the same mesh. The validity and stability of the proposed method are verified by numerical examples of one and two dimensions problems.
